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I have a dataset consisting of irregularly spaced points in the ocean. For each point I have coordinates and a data value. I need to interpolate to a regular grid. So far, so easy.

There are areas of land within the area covered by the dataset, and in the original dataset there are simply no points there. I have polygons of the land boundaries.

I need to exclude the land from the output. This is fairly straightforwardly accomplished by checking which of the points on the target grid are within the polygons and removing them. However, I also need to make sure that whatever interpolation technique is used does not consider points that are (for example) the other side of a peninsula - potentially a short distance away in a straight line, but a long way (or possibly not connected at all) by sea.

I'm sure that this must be a solved problem - I imagine any GIS package will have a way to deal with it - but I am at a loss as to what search terms to use in looking for the solution.

I have been debating whether to ask this question here, or on stats.SE, or on GIS.SE, or on Stackoverflow... but let's see how it goes.

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A very neat approach for optimal interpolation, which consider not only breaklines along the coast but also anisotropies caused by currents and horizontal diffusion, was given by Lynch & McGillicuddy (2001). Their approach is quite elegant and takes advantage of the finite element methodology to avoid the transfer of information across boundaries.

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    $\begingroup$ Oh, that is clever. It's possibly not fully appropriate for the current task, and there's no way that I have time to try to implement it, but I'll file the paper away for future reference. Thanks! $\endgroup$ – Semidiurnal Simon Jul 17 '14 at 15:54
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Depending on the nature of the data, the approach of

Hess, K., R. Schmalz, C. Zervas, and W. Collier, 2004. 'Tidal Constituent and Residual Interpolation (TCARI): A New Method for the Tidal Correction of Bathymetric Data'. NOAA Technical Report NOS CS 4, Silver Spring, MD, 112 pp.

(http://www.nauticalcharts.noaa.gov/staff/docs/TCARI_CS4.pdf)

might be appropriate. This boils down to solving a diffusion equation on an unstructured grid of the domain (TCARI also adds in some additional terms to help extrapolate trends in the data rather than a zero-gradient condition at the shorelines). With just the diffusion problem, ~100 lines of python was enough to code this up for a San Francisco Bay domain with 500k cells used in the diffusion problem.

Simon Wood and his then PhD student David Lawrence have also done a fair bit of work in this area, though my impression of their methods is that they are fairly expensive computationally for dense ocean observations. (I'm going to feel silly if Simon W the asker is actually Simon Wood)

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  • $\begingroup$ grin No, I'm not Simon Wood. Thanks, that looks intersting - I don't have time to read it in detail now, but will add it to the to-read pile :-) $\endgroup$ – Semidiurnal Simon Jul 27 '14 at 7:01
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Partial answer: after some further research: It looks as though the terminology that I am looking for is "Breakline". I need to define my coastlines as being breaklines. Now I need to figure out how to implement them in the languages that I am using, but that's probably a question for GIS.SE or Stackoverflow.

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